In the last 3 years there has been a huge increase in the use of pore-scale modeling to study multiphase flow and transport in porous media. Starting from single pore models of fluid arrangements, computations of relative permeability, interfacial area, dissolution rate and many other physical properties have been made. Combined with a realistic description of the pore space, predictive modeling of a variety of processes, including waterflood relative permeability and mass transfer coefficients, is now possible. This review highlights some of the major advances, with an emphasis on models of wettability and three-phase flow.

Flow in porous media — pore-network models and multiphase flow

High resolution schemes for hyperbolic conservation laws

History matching is a type of inverse problem in which observed reservoir behavior is used to estimate reservoir model variables that caused the behavior. Obtaining even a single history-matched reservoir model requires a substantial amount of effort, but the past decade has seen remarkable progress in the ability to generate reservoir simulation models that match large amounts of production data. Progress can be partially attributed to an increase in computational power, but the widespread adoption of geostatistics and Monte Carlo methods has also contributed indirectly. In this review paper, we will summarize key developments in history matching and then review many of the accomplishments of the past decade, including developments in reparameterization of the model variables, methods for computation of the sensitivity coefficients, and methods for quantifying uncertainty. An attempt has been made to compare representative procedures and to identify possible limitations of each.

Recent progress on reservoir history matching: a review

Multi-scale finite-volume method for elliptic problems in subsurface flow simulation

The heterogeneous multiscale method (HMM), a general framework for designing multiscale algorithms, is reviewed. Emphasis is given to the error analysis that comes naturally with the framework. Examples of finite element and finite difference HMM are presented. Applications to dynamical systems and stochastic simulation algorithms with multiple time scales, spall fracture and heat conduction in microprocessors are discussed.

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The heterogeneous multiscale method

Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media

This paper describes hierarchical approach to modeling flow in a naturally fractured formation. Our model is based on calculating the effective permeability of a fractured formation, as a function of grid block size, and using the results in a conventional finite difference flow simulator. On the basis of their length (lf) relative to the finite difference grid size (lg), fractures are classified as belonging to one of three groups: (1) short fractures (lf≪ lg), (2) medium-length fractures (lf ∼ lg), and (3) long fractures (lf≫ lg). The effects of the fractures belonging to each class are computed in a hierarchical manner. The permeability contribution from short fractures is derived in an analytical expression and used as an enhanced matrix permeability for the next-scale (medium-length) calculation. The effective matrix permeability associated with medium-length fractures is numerically solved using a boundary element method. The long fractures are modeled explicitly as major fluid conduits. As numerical examples, tracer transport in fractured formations was illustrated. The numerical results clearly indicated that effective tensor permeability well represented directional, enhanced permeability in fractured formations. The fluid-conduit formulation captured the efficient fluid transport by long fractures.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2000WR900340

Hierarchical modeling of flow in naturally fractured formations with multiple length scales

We present a multiscale finite-volume (MSFV) method for multiphase flow and transport in heterogeneous porous media. The approach extends our recently developed MSFV method for single-phase flow. We use a sequential scheme that deals with flow (i.e., pressure and total velocity) and transport (i.e., saturation) separately and differently. For the flow problem, we employ two different sets of basis functions for the reconstruction of a conservative fine-scale total velocity field. Our basis functions are designed to have local support, and that allows for adaptive computation of the flow field. We use a criterion based on the time change of the total mobility field to decide when and where to recompute our basis functions. We show that at a given time step, only a small fraction of the basis functions needs to be recomputed. Numerical experiments of difficult two-dimensional and three-dimensional test cases demonstrate the accuracy, computational efficiency, and overall scalability of the method.

Seong H. Lee

Papers

Multi-scale finite-volume method for elliptic problems in subsurface flow simulation

Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media

Hierarchical modeling of flow in naturally fractured formations with multiple length scales

Adaptive Multiscale Finite-Volume Method for Multiphase Flow and Transport in Porous Media

Adaptive fully implicit multi-scale finite-volume method for multi-phase flow and transport in heterogeneous porous media